Problem: Solve for $z$, $ \dfrac{5z + 7}{4z + 1} = 4$
Solution: Multiply both sides of the equation by $4z + 1$ $ 5z + 7 = 4(4z + 1) $ $5z + 7 = 16z + 4$ $7 = 11z + 4$ $3 = 11z$ $11z = 3$ $z = \dfrac{3}{11}$